Finite-time stable estimator for attitude motion in the presence of bias in angular velocity measurements

Abstract

This article presents a nonlinear finite-time stable attitude estimation scheme for a rigid body with unknown dynamics and with unknown bias in angular velocity measurements. The attitude and angular velocity are estimated from a minimum of two linearly independent known vectors measured in the body-fixed frame, and the measured angular velocity vector is assumed to have a constant bias in addition to measurement errors. The estimated attitude evolves directly on the special orthogonal group SO(3) of rigid body rotations, avoiding any ambiguities and singularities. The constant bias in angular velocity measurements is also estimated. The estimation scheme is proven to be almost globally finite time stable in the absence of measurement errors using a Lyapunov analysis. The robustness of the scheme in the presence of bounded measurement errors is analytically shown. The estimation scheme is discretized as a geometric integrator for digital implementation. Numerical simulations demonstrate the finite time stability properties of the estimation scheme. Robustness of this estimation scheme is also demonstrated through a numerical comparison against some state-of-the-art nonlinear attitude estimation schemes.